Question

Estimate the population of bacteria at 9 hours.
Time (hours) 0 1 2 3 4 5 6
Population (1000s) 5.1 3.03 1.72 1.17 1.38 2.35 4.08

Answer 1

@xapproachesinfinity

Answer 2

did you try drawing this!

Answer 3

to see what kind of graph it might be

Answer 4

No, i don't know where to start. But i do have to show my work

Answer 5

well look for an online plotter
put all of those points then post the picture you got here

Answer 6

ok one second

Answer 7

this looks like a polynomial to me!

Answer 8

http://www.wolframalpha.com/input/?i=%280%2C5.1%29+%281%2C3.03%29%2C+%282%2C1.72%29%2C+%283%2C1.17%29%2C+%284%2C1.38%29%2C+%285%2C2.35%29%2C+%286%2C4.08%29

Answer 9

When the numbers are given in equal intervals, another way is to calculate the differences of the given numbers. If the differences are not constant, it means that the function does not represent a straight line.
However, you can calculate the differences of the previously calculated differences. If the second difference is constant, the function is a quadratic. You can then continue the sequences to find f(9).

Answer 10

How do i keep it going to find the answer for 9 hours though

Answer 11

the second difference is constant 0.76
so it really is a quadratic

Answer 12

so how do we use the quadratic to find the answer? im confused and need to show my work

Answer 13

there is a different method then the sequence
f(x)=ax^2+bx+c
f(0)=5.1
f(1)=3.03
f(2)=1.17
you got 3 equation in terms of a,b,c
solve for them

Answer 14

if you got the equation
you plug 9
for f(9)

Answer 15

A=3.8 B=-2.45 and C=5.1

Answer 16

no no

Answer 17

I had to find that in the question previous to this one

Answer 18

Are we doing it differently because we are plugging in the 9?

Answer 19

you have to find a,b , and c plug 0 for one equation
1 for the second
2 doe the third
system of three equation

Answer 20

f(0)=5.1=c
actually c is good!

Answer 21

how did you find b and a

Answer 22

f(1)=3.03=a+b
f(2)=1.72=4a+2b

Answer 23

oh i forgot c
a+b+c=3.03
4a+2b+c=1.72

Answer 24

c=5.1

Answer 25

Ok i've written what we have so far

Answer 26

solve that for a and b

Answer 27

4a+2b=-3.38?

Answer 28

yes!
now you have two equation
solve for a and b

Answer 29

i got a=0.38
b=-2.45

Answer 30

thats what i have

Answer 31

so we have f(x)=0.38x^2-2,45x+5.1

Answer 32

http://prntscr.com/7odnai
looks like the shape we have before

Answer 33

plug in 9 for f(9)

Answer 34

How do i do that though ? thats where i get lost

Answer 35

f(9)=0.38 (9)^2-2.45(9)+5.1

Answer 36

you just replace x by 9

Answer 37

oh ok, one sec im gonna calculate

Answer 38

F= 30.78-22.05+5.1

Answer 39

we need final value what is it?

Answer 40

13.83

Answer 41

yes!

Answer 42

that's the number of bacteria after 9hours in thousands

Answer 43

So thats our final answer 13.83? :)